Domain Definition and 704 Threads

Homework Statement I need to compute the following using the Jacobian: \int\int_D \frac{x-y}{x+y} dxdy Where D = \left\{(x,y):x\geq 0, y\geq 0, x+y \leq 1\right\} Homework Equations The Attempt at a Solution I've made the transformation: s=x+y \qquad t = x-y My problem is finding the...

Hi, I am trying to understand the impact of cut off frequency on the gain and trying to relate it in time domain but unable to do so. For e.g., I have built a single pole RC filter wherein R and C values are chosen to match the cut off frequency of 1K (R = 10KΩ/C = 16nF). The input is a square...

Homework Statement See attached file. Homework Equations The Attempt at a Solution I've only been able to do part (a) of this question. I ended up with: tanz= i ({\frac{1-e^{(2iz)}}{1+e^{(2iz)}}}) I'm not sure how to approach the next two parts. If anyone could give me any...

Homework Statement Consider a lamina (two dimensional plate) with edges given by the lines y = sqrt(x) and y = -x + 2x^(2), for which the density is given by P(x; y) = x. (a) Define the domain of the lamina as the union of a Type 1 region and a Type 2 regions. b) Calculate the mass. Just...

Homework Statement f(x,y)=2x3-2y3-3x2 K={(x,y)\inℝ2:x2+y2≤5,y≤0} Find the maximum and minum of f(x,y) within K. Homework Equations ∇f(x,y)=(6x2-6x,-6y) Hess(f)=diag(12x-6,-6) (relevant?) The Attempt at a Solution What I've done so far was calculate the pair(s) (x,y)...

I am trying to show that $\mathbb{Z}[\sqrt{-3}]$ is not a euclidean domain, now I know that in every euclidean domain we have that an element is prime iff it is irreducible so I need to find an irreducible element of $\mathbb{Z}[\sqrt{-3}]$ that is not prime, I can't seem to think of one...

I keep reading through the course textbook but no matter how many times I read it I just can't see the understanding of it? There are activities asking me to solve problems, and I have a book of exercises to do, but the main book supposed to be designed to give some information to the student...

Just for clarification, I was wondering if someone could clarify what the difference between a magnetic moment and magnetic domain is. My understanding is a magnetic moment is when the atom aligns it's subatomic particles relative to the magnetic field, and that a magnetic domain is groups of...

Hello, I need to sketch the frequency domain for the following AM waveform showing total bandwidth and frequency. 8sin(2pi500kt - 4cos(2pi530kt) + 4cos(2pi(470kt) I have attached an attempt I have made. Does anyone know if I have this correct or not ? Thanks kindly for any input.

I need a physical explanation of s domain..Is s-domain a higher dimensional plane..?

I'm curious if anyone knows why my calculator would return "Domain Error" when calculating (-i)^4 on my TI-36X Pro? ((-i)^2)^2 works just fine on the machine, and (-i)^4 works just fine on my TI-83 Plus. Any ideas?

1. Evaluate the integral ∫VxdV inside domain V, where V is bounded by the planes x=0, y=x, z=0, and the surface x2+y2+z2=1 Answer given: 1/8 - √2/16 (which is NOT what I got.. ) 2. The attempt at a solution Ok, it's a triple integral, I know this. ∫dx runs from 0 to 1 ∫dy...

gcd(a,b) unique in Euclidean domain?? Homework Statement In Hungerford's Algebra on page 142, the problem 13 describes Euclidean algorithm on a Euclidean domain R to find THE greatest common divisor of a,b in R. My question is that does this THE mean THE UNIUQE? I've heard from my lecturer in...

√Homework Statement √(log1/5(1/Sin5x)) Log to the base 1/5*(1/Sin5x) FIND THE DOMAIN I have an answer to this solution, I Just need some help with understanding it :(... and also could someone tell me if info is missing. f(x) = √(log1/5(1/Sin5x)) Restrictions: 1/sin5x ǂ...

Hi, I am wondering how to express the domain of a two-variable function f(x,y) as below. For any given y, f(x,y) is defined on [0, g(y)); for any given x, f(x,y) is defined on [0, h(x)). Then how should I specify the domain for the function f(x,y)? To be more specific, f(x,y)=x+y, and...

Homework Statement Two waves on a string are given by the following functions: Y1 (x,t) = 4cos(20t-x) Y2 (x,t) = -4cos(20t+x) where x is in centimeters. The waves are said to interfere constructively when their superposition |Ys| = |Y1 + Y2| is a maximum and they interfere destructively when...

for example if f(x) = \frac{x^{2} - 1}{x+1} they by factoring: f(x) = \frac{x^{2} - 1}{x+1} = \frac{(x + 1)(x - 1)}{x+1} = x - 1 thus the simplified version is x - 1 let's say g(x) = simplified f(x) g(x) = x - 1 meaning g(x) = f(x) but g(-1) ≠ f(-1) am I missing something?

I know that, for k an integer, the rose polar curve expressed by r=r(θ)= cos(kθ) has a period of π if k is odd and 2π if k is even (usually expressed as saying that there are k distinct petals if k is odd, and 2k petals if k is even). However, I have yet to pin down the reason for this...

So I've done some problems where a sphere intersects with a cylinder and I needed to find the volume of the intersected region using triple integrals. For example, if I needed to find the domain of integration for the intersection of the sphere $$x^2+y^2+z^2=a^2$$ and the cylinder...

Homework Statement Given the function, state the domain and range. I just want to make sure my notation is correct? More specifically, the I am f, can you have the independent variable in there? Here's my answer: http://tinypic.com/r/2nlda2q/5 Homework Equations The...

1. I was asked to roughly sketch a graph given the information seen, in the below picture, to the right of the graph. 2. My actual graph is done by hand and the lines are not as straight, but the general shape is the same. Does it look approximately right? The areas I am worried...

Homework Statement State the domain and range of the function that models each half of the roof (triangle) Homework Equations Y= -0.7x+1.9 (left half) Y= 0.7x+1.9 (right half) The Attempt at a Solution Why is the answer: Left half: domain: −2.7≤x≤0 range: 0≤y≤1.9 Right...

As we know , the average value of a function over is : i wanted to calculate the average value of a function over its entire domain ( e.g ) firstly, i divided the interval into 2 intervals & and calculated the F_avg for each ,,, is my way correct ? thanks !

In the first volume of Differential Geometry, Ch. 1, Spivak states that if U \subset \mathbb{R}^n is homeomorphic to \mathbb{R}^n, then U is open. This seems obvious: \mathbb{R}^n is open in \mathbb{R}^n, so its pre-image under a homeomorphism f:U \rightarrow \mathbb{R}^n is open. The pre-image...

Did you know first internet domain was registered exactly 27 years ago, on March 15th? http://symbolics.com/

[b]1. what is the domain of the function k(y)=1/(2y+1)? Express your answer in interval notation [b]2. [b]3. I find that 0.5 is a possibility in this function, but since i have not done functions at school, i do not really know much more of this question.

Hi everyone, I'm currently looking to solve an equation of the general form: \sqrt{x^2-y^2}+\sqrt{\epsilon x^2-y^2} = \beta. I'm interested in solving this equation for x assuming y>0, \epsilon>1 and \beta \in \mathbb{C}. By squaring the equation twice I can find four potential solutions of...

Homework Statement so I am supposed to find the domain of the function, the range, describe its level curves, find the boundary of the functions domain, determine if the boundary is an open region, a closed region, or neither, and decide it the domain is bounded or unbounded...

Homework Statement x*sin(sqrt(x^2+y^2))/sqrt(x^2+y^2) find the domain of continuity Homework Equations none The Attempt at a Solution I found the domain, which is x^2+y^2 > 0 and since x^2 >= 0 and y^2 >= 0 therefore the domain is (-inf,0) (0,inf) but the professor then asked...

Homework Statement I'm trying to write a proof ot demonstrate that every finite domain contains an identity element.Homework Equations The Attempt at a Solution If I can think of the operation from the ring as a mapping...like x->yx..where y are just values from the domain and then to consider...

How can I prove that every finite domain has an identity element? How should I think about the problem and what should I take into consideration?

Okay i need to find expressions for v1 and v2 and I am using nodal analysis: these are not the final the equations just initial equations by first look I am good finding expression for v1, (2/s)-(v1/1)-((v1-v2)/(2/s)) = 0 Where i am stuck is with the current source and 2 ohm res...

Is this claim true? Assume that X,Y are topological spaces, and that all closed subsets of X are compact. Then all continuous bijections f:X\to Y are homeomorphisms. It looks true on my notebook, but I don't have a reference, and I don't trust my skills. Just checking.

I'm asked to find the domain of 1/[e^(x+y)-3] Which means I'm solving for e^(x+y)>=3 But how would I go about solving this?

Homework Statement The problem is: for all 0≤a≤1 so i need to find the domain Homework Equations N/A The Attempt at a Solution I tried it like this: yet my solution is wrong,i am not so sure why. wolfram gives me this;

Homework Statement f(x) = (arctan(ln(sqrtx - 1)))^3 Homework Equations domain of arctan: all real numbers range of arctan: -∏/2, ∏/2 The Attempt at a Solution I know that domain is x>0 when x ≠ 1, because I need a positive number to go under the radical and the natural log of 0 is...

(note: I posted this here instead of the Biology forum because the topic involves heavy quantum concepts that mere biologists can't handle) I read PF Mentor Ryan_m_b mentioned elsewhere that "Discussing quantum effects in biology is not a banned topic on this forum, however threads that...

The problem ask me to find the tension on a capacitor after a switch has been opened. I have everything in terms of equations in s-domain and I'm sure they aren't wrong because I checked on the book. My unique problem is to understand a certain passage necessary to find the voltage knowing...

Homework Statement Let S be the open unit disk of radius 2 centered at the origin. T is a subset of the real axis. The set R is obtained by removing T from S. Is R a domain when: 1. T is the line segment {z\in ℂ | Re(z) ≤ 1 and Im(z) = 0} 2. T is the line segment {z\in ℂ | Re(z) < 2 and...

Hi. Under what conditions does the following equality hold? f(x)=\lim\limits_{\Omega\rightarrow\{x\}} \frac{1}{\mu(\Omega)}\int_\Omega f d\mu where \mu is some measure. Being a little more careful, let \Omega_i be a sequence of sets such that \Omega_{i+1}\subseteq\Omega_i and...

Homework Statement The function f:x→ 4-x2 for the domain x≤0. Find the inverse of is denoted by f-1 and state the domain and range of f-1. Homework Equations Set equation to 0 and solve for x to find inverse. The D and R is going to be switched for the inverse..? The Attempt at a...

Homework Statement The function f has domain (-∞, ∞) and is defined by f(x) = 3e2x. The function g has domain (0, ∞) and is defined by g(x) = ln 4x. (a) Write down the domain and range of f∘g. (b) Solve the equation (f∘g)(x) = 12 2. The attempt at a solution (a) Is it correct...

Hi guys, I'm really confused in finding the domain of quadratic equations. For example: when finding a suitable domain so that an inverse exists, why is the domain of x2-4 x>0 whilst, the domain of 2x2+3 is x≥0 Can the domain of x2-4 be x≥0? Furthermore, what is the largest domain and how do...

hi all, i am getting the above problem while executing my fortran program. please help me how to fix it. thank MNM

if i am being asked to write the domain of integration in a triple integral problem in a cartesian form , may i used polar coordinates to express instead of x and y? thank you

This is a problem from the Boyce and Diprima Elementary DE book. I solved this equation and got the correct solution. However, the author notes that the solution is defined on the interval (-2,3) only. I have found it to be defined (-inf,-2)u(-2,3)u(3,inf), or EVERYWHERE BUT x=-2, x=3. Is...

What are the domain and range of the following: (Note: It is a relation that is not a function.) y^2(x^2 - 1) = x^4

in interval notation? y^2(x^2 - 1) = x^4 (This is my own problem.)

Homework Statement Use set or interval notation to give the domain of the function: g(t)=(x-5)/sinx Homework Equations The Attempt at a Solution So looking at this, I recognize that x cannot be 0,180,360, etc... it's just putting this into set or interval notation that...

Hello all, I want to filter DC offset for a signal by applying a high-pass filter to it (I've been told that to filter the DC offset this is what I should do - I'm not sure why exactly!) My question is; do I do that in the time-domain or frequency-domain after applying FFT? And I would...